Читать книгу Geochemistry - William M. White - Страница 55

As we shall see, knowledge of the heat capacity of substances turns out to be critical to determining properties such as enthalpy and entropy, and, ultimately, to predicting chemical equilibrium. The heat capacity of a substance reflects the internal motion of its atoms. There are three kinds of motion available to atoms and molecules: translational, vibrational and rotational,† but often one or more of these modes will not be available and not contribute to the energy of a substance. For gases at low temperature, only rotational and translational motions are important (for a monatomic gas, only translational modes are available), while only vibrational motions are important for solids (translational modes are available to solids, which is why solids have finite vapor pressures, but they are extremely improbable, which is why vapor pressures of solids are very small and can usually be neglected). Twice as much energy is typically required to raise the temperature of a vibrational mode by 1 K as for a translational mode. This is because vibration involves both kinetic and potential energy of two or more atoms. Also, vibrational modes do not accept much energy at low temperatures.

This latter phenomenon is not predicted by classical physics; as a result, nineteenth-century physicists were puzzled by the temperature dependence of heat capacity. In 1869, James Maxwell referred to the problem as “the greatest difficulty yet encountered in molecular theory.” The solution required a more radical revision to physics than Maxwell imagined: the heat capacity problem turned out to be one of the first indications of the inadequacy of classical physics.

An understanding of the dependence of heat capacity on temperature was only achieved in the twentieth century with the aid of quantum physics. A complete theoretical treatment of heat capacity of real substances is beyond the scope of this book. However, even the few statements we will make will require us to make another excursion into statistical mechanics, a closely related field, to discover the Boltzmann distribution law. What we learn will be of considerable use in subsequent chapters.